If you wanted the pilot to go directly to the next point then why not use "direct to" instead?
The implied meaning of "own nav" would be directly to the next appropriate tracking point. We use this phrase when terminating a vectoring service; to confirm to the pilot to stop flying the heading even if it happens to be the exact same track... From a controller perspective it wouldn't mean "free to wonder" it would mean proceed direct to "X". An example would be "Resume own Navigation to Dublin" this means point directly at Dublin... Some are lazy and just say "own nav" but the intent would be the same.
Generally we consider the capabilities of the user regarding ability to track direct; eg a C152 VFR will not be treated the same in terms of nav ability (expectations) as the A380 etc.